WASHINGTON — The fate of President Barack Obama's health care overhaul was cast into deeper jeopardy Tuesday as the Supreme Court's conservative justices sharply and repeatedly questioned its core requirement that virtually every American carry insurance. The court will now take up whether any remnant of the historic law can survive if that linchpin fails.

The justices' questions in Tuesday's hearing carried deeply serious implications but were sometimes flavored with fanciful suggestions. If the government can force people to buy health insurance, justices wanted to know, can it require people to buy burial insurance? Cellphones? Broccoli?

The law, pushed to passage by Obama and congressional Democrats two years ago, would affect nearly all Americans and extend insurance coverage to 30 million people who now lack it. Republicans are strongly opposed, including the presidential contenders now campaigning for the chance to challenge Obama in November.

The court focused on whether the mandate for Americans to have insurance "is a step beyond what our cases allow," in the words of Justice Anthony Kennedy.

But Kennedy, who is often the swing vote on cases that divide the justices along ideological lines, also said he recognized the magnitude of the nation's health care problems and seemed to suggest they would require a comprehensive solution.

He and Chief Justice John Roberts emerged as the apparent pivotal votes in the court's decision. The ruling is due in June in the midst of a presidential election campaign that has focused in part on the new law.

Though many of the justices asked tough questions and made strong statements, past cases have shown that those don't necessarily translate into votes when it comes time for a decision.

Wednesday's final arguments – the third day in the unusually long series of hearings – will focus on whether the rest of the law can remain even if the insurance mandate is struck down and, separately, on the constitutionality of another provision expanding the federal-state Medicaid program.

The insurance requirement is intended to complement two unchallenged provisions of the law that require insurers to cover people regardless of existing medical conditions and limit how much they can charge in premiums based on a person's age or health.

The law envisions that insurers will be able to accommodate older and sicker people without facing financial ruin because the insurance requirement will provide insurance companies with more premiums from healthy people to cover the increased costs of care.

The biggest issue, to which the justices returned repeatedly during two hours of arguments in a packed courtroom, was whether the government can force people to buy insurance.

"Purchase insurance in this case, something else in the next case," Roberts said.

"If the government can do this, what else can it not do?" Justice Antonin Scalia asked. He and Justice Samuel Alito appeared likely to join with Justice Clarence Thomas, the only justice to ask no questions, to vote to strike down the key provision of the overhaul. The four Democratic appointees seemed ready to vote to uphold it.

Kennedy at one point said that allowing the government mandate would "change the relationship" between the government and U.S. citizens.

"Do you not have a heavy burden of justification to show authorization under the Constitution" for the individual mandate? asked Kennedy.

At another point, however, he also acknowledged the complexity of resolving the issue of paying for America's health care needs.

"I think it is true that if most questions in life are matters of degree ... the young person who is uninsured is uniquely proximately very close to affecting the rates of insurance and the costs of providing medical care in a way that is not true in other industries. That's my concern in the case," Kennedy said.

Roberts also spoke about the uniqueness of health care, which almost everyone uses at some point.

"Everybody is in this market, so that makes it very different than the market for cars or the other hypotheticals that you came up with, and all they're regulating is how you pay for it," Roberts said, paraphrasing the government's argument.

Solicitor General Donald Verrilli Jr. sought to assure the court that the insurance mandate in the Patient Protection and Affordable Care Act that Obama signed into law in 2009 is a key part of the law's goal of reaching many of the more than 40 million people who don't have health insurance through their employers, don't qualify for government aid and cannot afford to buy coverage on their own.

Paul Clement, who is representing Florida and 25 other states in challenging the law, called the mandate "an unprecedented effort by Congress."

Clement, a predecessor of Verrilli's as solicitor general, said the requirement would force people, especially those who are young and healthy, to buy a product they don't want.

Michael Carvin, representing the National Federation of Independent Business in opposing the law, also pushed hard on the notion of individual freedom. When Justice Stephen Breyer asked if the federal government could not order vaccinations "if there was some terrible epidemic sweeping the United States," Carvin said no. Congress lacks the power to do so, he said.

Justice Ruth Bader Ginsburg said she found the debate over health care similar to an earlier era's argument about the Social Security retirement system. How could Congress be able to compel younger workers to contribute to Social Security but be limited in its ability to address health care? she wondered.

"There's something very odd about that, that the government can take over the whole thing and we all say, oh, yes, that's fine, but if the government wants to preserve private insurers, it can't do that," she said.

Scalia and Roberts noted that the health care overhaul law would make people get insurance for things they may not need, such as heart transplants or pregnancy services. "You can't say that everybody is going to participate in substance abuse services," Roberts said.

On the other hand, Ginsburg said, "The people who don't participate in this market are making it more expensive for those who do."

"You could say that about buying a car," Scalia retorted, noting that if enough people don't buy cars the cost could go up.

But, unlike cars, almost everyone eventually will be required to use the health care system, Verrilli said in defense of the law. Without health insurance, he said, "you're going to the market without the ability to pay for what you're going to get."

Members of Congress on both sides of the fight sat through Tuesday's arguments, along with Attorney General Eric Holder and Health and Human Services Secretary Kathleen Sebelius. Republicans opposed to the law in the audience included Senate Minority Leader Mitch McConnell of Kentucky, Sen. John Cornyn of Texas and Sen. Lindsey Graham of South Carolina. Also at the court were Democratic supporters including Sen. Pat Leahy of Vermont, Sen. Max Baucus of Montana and Reps. John Dingell and John Conyers, both of Michigan.

Demonstrators returned Tuesday to the sidewalk outside the Supreme Court, with more than 100 supporters of the law circling and chanting, "I love Obamacare." They carried signs reading slogans such as "A healthy America is a productive America" and `'Protect the law."

More than a dozen opponents held a news conference criticizing the bill.

Supporters, two of them wearing Statue of Liberty costumes, marched to music played over a loudspeaker. A trumpet player played "When the Saints Go Marching In" and "This Little Light of Mine," and supporters changed the lyrics to ones supporting the health care law.

One demonstrator opposing the law wore a striped prison costume and held a sign, "Obama Care is Putting the US Tax Payer in Debtors Prison."

Rep. Michele Bachmann of Minnesota, a former Republican presidential candidate, joined a tea party press conference of opponents of the law. Calling the law "the greatest expansion of federal power in the history of the country," she said, "We are calling on the court today: Declare this law unconstitutional."